Conditions for well-posedness in Gevrey classes of the Cauchy problems for Fuchsian hyperbolic operators (Q1071176)

\textit{H. Tahara} [J. Fac. Sci., Univ. Tokyo Sect. I A 27, 465-507 (1980; Zbl 0463.35053)] studied the Cauchy problem for Fuchsian hyperbolic equations with \(C^{\infty}\) coefficients and established the \(C^{\infty}\) well-posedness. In the present paper the same problem is discussed in Gevrey classes \(\gamma^{(k)}_{loc}\). The author proves well-posedness if k is smaller than a number s(P) which is closely connected with the Fuchsian operator P.